The characterization of semigroups that could be embedded into an inverse semigroup was solved by Boris M. Schein in 1958, setting a trajectory for a career defined by rigorous advancements in algebraic structures. A mathematician whose work navigated the complexities of geometry and transformation semigroups, he held dual citizenship while bridging academic research between the Soviet Union and the United States.
Early Education and Research at Saratov
Born in Moscow on 22 June 1938, Schein relocated to Saratov during World War II. He pursued undergraduate studies in Mechanics-Mathematics at Saratov State University, specializing in geometry under the guidance of Viktor Wagner. By 1960, he graduated summa cum laude. He later focused his doctoral research on semigroups of transformations, defending his candidacy dissertation in 1962 and his Doctor of Sciences thesis in 1966 at Herzen State Pedagogical University in Saint Petersburg.
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Schein became a founding editor of the journal Semigroup Forum in 1968, published by Springer-Verlag. During the 1970s, he encountered significant political barriers due to his international collaborations. Authorities restricted his correspondence with foreign mathematicians and obstructed his students from completing their degrees. Following the retirement of his mentor, Viktor Wagner, Schein was dismissed from his faculty position at Saratov.
Academic Contributions in the United States
In 1979, Schein emigrated to Austria, eventually securing a visiting appointment at Tulane University in New Orleans. By 1980, he joined the University of Arkansas, where he eventually served as a Distinguished Professor in the Department of Mathematical Sciences. His research introduced the Schein index, a metric used to determine the minimum number of concepts required to represent a binary relation's logical matrix as a Boolean sum.
Professional Recognition
Beyond his teaching duties and original research, Schein maintained an active role in the mathematical community. In 2011, the European Mathematical Society recognized his service by naming him a distinguished reviewer of Zentralblatt MATH. He remained a central figure in semigroup theory until his death on 4 October 2023, at the age of 85.
Fast facts
- Born: 22 June 1938, Moscow
- Died: 4 October 2023, age 85
- Field: Geometry and semigroups
- Education: Saratov State University, Herzen University
- Key academic roles: Distinguished Professor, University of Arkansas
- Citizenship: Russia, Soviet Union, United States
Questions readers ask
What is the Schein index?
It is the minimum number of concepts required to express the logical matrix of a binary relation as a Boolean sum.
Where did he hold his final academic position?
He served as a Distinguished Professor in the Department of Mathematical Sciences at the University of Arkansas.
Achievements
- Held posts at Tulane University and University of Arkansas
- Fields: geometry
